In Ginza, I bought some musk melons as gifts at Ginza Sembikiya. I believe there were also some at the depachika in Ginza Mitsukoshi (but I might be getting it confused with the Nihombashi location). I’m sure that there are other shops, too, but this one was convenient for me.
At Sembikiya, there’s also a fruit parlor with snacks including a musk melon parfait (I didn’t try it).
That’s not true. Generally, those in the stores here are not fully ripe yet. You leave it outside of refrigerator for few days until the bottom turns soft. Then put it in refrigerator for a day or two before you consume it. As good as Hayato’s and the one we had in Japan.